Question

identify the interval where the function is increasing. 3<x<6 -2<x<0 x>3 x>-2

Explanation:

Step1: Understand the concept of increasing function

A function \(y = f(x)\) is increasing on an interval if, for any two points \(x_1\) and \(x_2\) in the interval with \(x_1

Step2: Analyze the graph

Looking at the parabola (quadratic function \(y = ax^{2}+bx + c,a>0\)), its vertex form is \(y=a(x - h)^{2}+k\). The axis of symmetry is \(x = h\). For a parabola \(y = ax^{2}+bx + c\) with \(a>0\), the function is decreasing on the interval \((-\infty,h)\) and increasing on the interval \((h,\infty)\).
From the graph (by observing the direction of the curve), the vertex (minimum point) occurs at \(x = 3\).
So, the function is increasing for \(x>3\).

Answer:

$x>3$